A Measuring Method for Nano Displacement Based on Fusing Data of Self-Sensing and Time-Digit-Conversion

Accurate and rapid measuring methods for displacement of nano-scale is necessary for manipulation. Self-sensing and time-digit-conversion(TDC) are two applicable measuring methods especially suitable for room-limited workspaces and vacuum-compliance required applications, thanks to their space-saving advantage and slight thermal impact on system. The self-sensing method gives measurements in high resolution at high sampling rate but its accuracy suffers from nonlinearity, while TDC has better linearity which causes less deviation to results but has a much lower sampling rate. A Kalman filter based fusion approach with dual estimation modes and self-adaptive parameters is designed to fuse the two measurements with different sampling rates at a higher frequency. Modifications to error covariance parameters are applied to traditional Kalman filter so that sensors' generalized errors rather than their Gaussian noises are taken into consideration, and corresponding derivation is given. A series of experiments are conducted to evaluate the performance of the fused measurement.